A graphical approach to multi-locus match probability computation: revisiting the product rule

Area of Science:

• Population Genetics
• Statistical Genetics
• Bioinformatics

Background:

• Allele frequencies at unlinked loci can be statistically non-independent due to genealogical relationships within finite populations.
• Understanding these dependencies is crucial for accurate genetic analysis, particularly in forensic and population studies.

Purpose of the Study:

• To introduce a flexible graphical method for computing multi-locus haplotype and genotype match probabilities in finite, randomly mating populations.
• To generalize existing methods for analyzing dependency effects in multi-locus match probabilities.
• To investigate the impact of mating models, specifically monogamy, on these probabilities.

Main Methods:

• Development of a novel graphical approach to model genealogical relationships and allele non-independence.
• Computation of probabilities for identical haplotypes or genotypes between two individuals across multiple loci.
• Extension of the analytical framework to accommodate various mating structures beyond random mating.

Main Results:

• The study demonstrates that monogamous mating systems significantly increase the probability of genotypic matches at unlinked loci compared to random mating.
• The magnitude of this increase is shown to be dependent on the number of loci (L) analyzed.
• A conjecture is proposed regarding a sharp upper bound for the effect of monogamy on match probabilities for a given L.

Conclusions:

• Genealogical structure is a critical factor influencing statistical independence of alleles.
• The developed graphical method provides a powerful tool for calculating multi-locus match probabilities under different mating models.
• Monogamy demonstrably elevates genotypic match probabilities, with the effect amplifying as the number of loci increases, highlighting the importance of considering mating systems in genetic analyses.